zunmbr.f (3) - Linux Man Pages

zunmbr.f -

SYNOPSIS

Functions/Subroutines

subroutine zunmbr (VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
ZUNMBR

Function/Subroutine Documentation

subroutine zunmbr (characterVECT, characterSIDE, characterTRANS, integerM, integerN, integerK, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( ldc, * )C, integerLDC, complex*16, dimension( * )WORK, integerLWORK, integerINFO)

ZUNMBR

Purpose:

If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      Q * C          C * Q
TRANS = 'C':      Q**H * C       C * Q**H

If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C
with
SIDE = 'L'     SIDE = 'R'
TRANS = 'N':      P * C          C * P
TRANS = 'C':      P**H * C       C * P**H

Here Q and P**H are the unitary matrices determined by ZGEBRD when
reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q
and P**H are defined as products of elementary reflectors H(i) and
G(i) respectively.

Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the
order of the unitary matrix Q or P**H that is applied.

If VECT = 'Q', A is assumed to have been an NQ-by-K matrix:
if nq >= k, Q = H(1) H(2) . . . H(k);
if nq < k, Q = H(1) H(2) . . . H(nq-1).

If VECT = 'P', A is assumed to have been a K-by-NQ matrix:
if k < nq, P = G(1) G(2) . . . G(k);
if k >= nq, P = G(1) G(2) . . . G(nq-1).

Parameters:

VECT

VECT is CHARACTER*1
= 'Q': apply Q or Q**H;
= 'P': apply P or P**H.

SIDE

SIDE is CHARACTER*1
= 'L': apply Q, Q**H, P or P**H from the Left;
= 'R': apply Q, Q**H, P or P**H from the Right.

TRANS

TRANS is CHARACTER*1
= 'N':  No transpose, apply Q or P;
= 'C':  Conjugate transpose, apply Q**H or P**H.

M

M is INTEGER
The number of rows of the matrix C. M >= 0.

N

N is INTEGER
The number of columns of the matrix C. N >= 0.

K

K is INTEGER
If VECT = 'Q', the number of columns in the original
matrix reduced by ZGEBRD.
If VECT = 'P', the number of rows in the original
matrix reduced by ZGEBRD.
K >= 0.

A

A is COMPLEX*16 array, dimension
(LDA,min(nq,K)) if VECT = 'Q'
(LDA,nq)        if VECT = 'P'
The vectors which define the elementary reflectors H(i) and
G(i), whose products determine the matrices Q and P, as
returned by ZGEBRD.

LDA

LDA is INTEGER
The leading dimension of the array A.
If VECT = 'Q', LDA >= max(1,nq);
if VECT = 'P', LDA >= max(1,min(nq,K)).

TAU

TAU is COMPLEX*16 array, dimension (min(nq,K))
TAU(i) must contain the scalar factor of the elementary
reflector H(i) or G(i) which determines Q or P, as returned
by ZGEBRD in the array argument TAUQ or TAUP.

C

C is COMPLEX*16 array, dimension (LDC,N)
On entry, the M-by-N matrix C.
On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q
or P*C or P**H*C or C*P or C*P**H.

LDC

LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).

WORK

WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

LWORK is INTEGER
The dimension of the array WORK.
If SIDE = 'L', LWORK >= max(1,N);
if SIDE = 'R', LWORK >= max(1,M);
if N = 0 or M = 0, LWORK >= 1.
For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L',
and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the
optimal blocksize. (NB = 0 if M = 0 or N = 0.)

If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.

INFO

INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

Author:

Univ. of Tennessee

Univ. of California Berkeley